I think that moment often divides people, and everyone interpretates the scene differently. I did feel bad for Hak, in all honesty. He was trying to get closer to her now that they've left behind their lives in the castle, but she didn't let him approach any further. I personally think that it's not only to keep her legacy alive but to preserve the current status of their relationship. She always thought that Hak's prime motivation to act as her bodyguard is out of a duty to her father. In a way, I think she's scared of a change. For some reason, this is one of my favorite moments b/w them though. Whatever way you interpretate that scene, it does highlight how important Hak is too Yona. The anime did a fantastic job at adaption this moment.
I agree with you. I felt bad for him, it was almost a Freudian slip that he called her by name, but I think you're right where it was almost like she's afraid of change. It might be that she sees him as someone super strong, and she wants desperately to be like him, and subconsciously, she's afraid that if their status changes, he'll change. I don't think she realizes that he wouldn't have joined the king if not for her first, then the Kings bravery. He was motivated by her first, I doubt she's realized it where I'm at.